What is the solution of the square root of 3x+28-8=x (-8=x is not in the square root) any explanation and answer is appreciated!
Answers
.. √(3x +28) -8 -x = 0
x = -4 . . . . . . from the graph
_____
If you add 8 and square both sides, you get
.. 3x +28 = (x +8)^2
.. x^2 +13x +36 = 0
.. (x +9)(x +4) = 0
.. x = -9 or -4 . . . . . . . the -9 solution is extraneous
Related Questions
Which table represents a quadratic relationship?
A .x -2 -1 0 1 2 3
f(x) 4 2 1 0.5 0.25 0.125
B. x -7 -6 -5 -4 -3 -2
f(x) 135 128 105 72 35 0
C. x -2 -1 0 1 2 3
f(x) -23.4 -23.2 -23 -22.8 -22.6 -22.4
D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
Answers
In each case, the x-values are equally-spaced. Thus looking at second differences will tell you if the relation is quadratic. If the second differences are non-zero and constant, then the values have a quadratic relationship.
A. First differences are 2-4 = -2, 1-2 = -1, 0.5-1 = -0.5. Second differences are -1-(-2) = 1, -0.5-(-1) = 0.5. Since 1 ≠ 0.5, this relation is not quadratic. (It is exponential with a base of 1/2.)
B. First differences are 128-135 = -7, 105-128 = -23, 72-105 = -33. Second differences are -23-(-7) = -16, -33-(-23)=-10. Since -16 ≠ -10, this relation is not quadratic. (It is cubic, since 3rd differences are constant at +4.)
C. First differences are -23.2-(-23.4) = 0.2, -23.0-(-23.2) = 0.2, -22.8-(-23.0) = 0.2. Second differences are zero, so this is not a quadratic relation. (It is linear, with a slope of 0.2.)
D. First differences are 56-90 = -34, 26-56 = -30, 0-26 = -26. Second differences are -30-(-34) = 4, -26-(-30) = 4. These are constant (=4), so the relation is quadratic.
The appropriate choice is ...
... D. x -1 0 1 2 3 4
... f(x) 90 56 26 0 -22 -40
Answer: D. x -1 0 1 2 3 4
f(x) 90 56 26 0 -22 -40
Step-by-step explanation:
Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?
Answers
General Idea:
We need to make use of the below formula to find the monthly payment..
[tex] Monthly \; Payment\; =\; \frac{P \times \frac{r}{12}}{(1-(1+\frac{r}{12})^{-m})} \\ \\ Where:\\ P\; is\; Principal\\ r\; is\; rate\; in\; decimal\; form\\ m\; is\; number\; of\; monthly\; payments [/tex]
Applying the concept:
Given:
[tex] P=\$224,500\\ r=4\%=0.04\\ m=30\; year \times 12 \; months/year=360\\ [/tex]
Substituting the given in the formula we will get the monthly payment.
[tex] Monthly\; Payment\; =\; \frac{224500 \times \frac{0.04}{12}}{(1-(1+\frac{0.04}{12})^{-360})} =\frac{\frac{8980}{12}}{(1-0.301796)} =\frac{748.3333}{0.698204} \\ \\ Monthly \; Payment= \$1071.7975 [/tex]
Conclusion:
The monthly payment during the initial period is $1072.
If g(x) is the inverse of f(x) and f(x) = 4x+12 what is g(x)?
Answers
Answer:
Inverse function: A function g is the inverse of a function f if whenever y=f(x) then x=g(y).
In other words, we can write this in terms of the composition of f and g as g(f(x))=x.
For any input x, the function corresponding to f spits out the value y=f(x)=4x+12.
Now, we want to find the inverse function g(x)=[tex]f^{-1}[/tex] that takes the value y as an input and spits out x as the output.
In other words, y=f(x) gives y as a function of x and we want to find [tex]x=f^{-1}(y)[/tex] that will give us x as a function of y.
Given,the expression y=4x+12 for y as a function of x and solve for x.
Subtract 12 from both sides we get;
y-12 = 4x+12-12
Simplify:
y-12 = 4x
Divide by 4 to both sides we get;
[tex]\frac{y-12}{4} =\frac{4x}{4}[/tex]
Simplify:
[tex]x=\frac{1}{4}y - 3[/tex]
therefore, [tex]x = f^{-1}(y) = \frac{1}{4}y-3[/tex]
since, g(x) is the inverse of f(x)
⇒[tex] g(x)=\frac{1}{4}x-3[/tex]
Now, verify that g(x) is really the inverse of f(x), we should show that the composition of f and g doesn't do anything to the input.
[tex](g o f)(x) = g(f(x)) = g(4x+12) = \frac{1}{4}(4x+12) -3 = x+3 -3[/tex]
Simplify:
g(f(x)) = x for all x
⇒ g(x) is the inverse of f(x)
Therefore, [tex] g(x)=\frac{1}{4}x-3[/tex]
Using inverse functions, it is found that that:
[tex]g(x) = \frac{x - 12}{4}[/tex]
To find the inverse function, we exchange x and y in the original function, then isolate f.
The function f(x) is given by:
[tex]f(x) = 4x + 12[/tex]
Function g(x) is the inverse of f(x), then:
[tex]y = 4x + 12[/tex]
[tex]x = 4y + 12[/tex]
[tex]4y = x - 12[/tex]
[tex]y = \frac{x - 12}{4}[/tex]
[tex]g(x) = \frac{x - 12}{4}[/tex]
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Part A: Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a total rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for x hours. (4 points)
Part B: Write the equation obtained in Part A using function notation. (2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
Answers
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\=\frac{42-26}{5-3} \\ \\=\frac{16}{2}=8[/tex]. A slope of 8 tells us that the hourly rental is $8. We can use this to back up and see what the rental fee is. When renting the kayak for 3 hours, Jake paid 26. We know that it costs $8 per hour; 8(3) = 24. This leaves us 26-24=$2 for the rental fee. The equation would then be
y = 8x + 2.
Writing this as a function would be f(x) = 8x + 2.
To graph this, we would label the x-axis as time (hours) and the y-axis as money (dollars). We would go up to the y-intercept, 2, and plot our point. (The y-intercept is 2 because in the form y=mx+b, b is the y-intercept; that's where our 2 is.) From here, we know the slope is 8=8/1, so we would go up 8 and over 1 to the right to plot our next point. Then we would draw our line between these two points.
Answer:
8x+2
fx= 8x+2
Step-by-step explanation:
please help im confused....
which ordered pair is a solution of the inequality?
2y+6<8
a. (4,13)
b. (-5,2)
c.(0,6)
d.(4,8)
Answers
Here is your answer:
The proper answer to this question is option D "(4,8)".
Your answer is D.
If you need anymore help feel free to ask me!
Hope this helps!
Triangle RST is congruent to triangle WXY. If the area of triangle WXY is 20 square inches, then the area of triangle RST is _____.
40 in2
10 in2
20 in2
80 in2
Answers
The area of triangle RST is also 20 20 square inches
What are congruent triangles?Triangles having equal side lengths and equal corresponding angles measures are called congruent triangles.
Given that, triangle RST is congruent to triangle WXY, the area of triangle WXY is 20 square inches,
We are asked to find the area of triangle RST,
Since, triangles RST and WXY are congruent, therefore, they will have congruent sides and angles,
That means, they will have equal area also,
ar (Δ RST) = ar (Δ WXY)
Therefore,
ar (Δ RST) = 20 square inches
Hence, the area of triangle RST is also 20 20 square inches
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Find the value of x. The diagram is not drawn to scale.
Answers
Answer:
C. [tex]x=99^{\circ}[/tex]
Step-by-step explanation:
We have been given a image. We are asked to find the value of x.
We can see that our given figure is a quadrilateral. We know that all interior angles of a quadrilateral add up-to 360 degrees.
[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
We can see that y and 116 degrees angles are linear angles, so we can set an equation as:
[tex]y^{\circ}+116^{\circ}=180^{\circ}[/tex]
[tex]y^{\circ}+116^{\circ}-116^{\circ}=180^{\circ}-116^{\circ}[/tex]
[tex]y=64^{\circ}[/tex]
Substitute [tex]y=64^{\circ}[/tex] in the equation:
[tex]x^{\circ}+y^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+64^{\circ}+125^{\circ}+72^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+261^{\circ}=360^{\circ}[/tex]
[tex]x^{\circ}+261^{\circ}-261^{\circ}=360^{\circ}-261^{\circ}[/tex]
[tex]x^{\circ}=99^{\circ}[/tex]
[tex]x=99[/tex]
Therefore, the value of x is 99.
which rule describes the translation PQR --> P'Q'R'?
Answers
The "Image" is the image that we ended with, so the blue triangle.
To determine how far we went from the pre image to the image, we can focus on one point, let's say point "P".
The pre image coordinates for point "P" are 2, 3.
The image coordinates for point "P'" are -1, 0.
To get from x value 2 to x value -3, we subtracted 3.
To get from y value 3 to y value 0, we subtracted 3.
So, our rule for this translation would be A, (x, y) ----> (x-3, y-3).
ASAP PLEASE:
Segment RS is congruent to segment DF. Which congruence statement is true?
- RS ≅ DF
- RS ≅ SFD
- RS ≅ SF
- RS ≅ RD
Answers
Answer:
A. [tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Step-by-step explanation:
We have been given a circle and we are told that segment RS is congruent to segment DF.
We can see that segment RS corresponds to arc RS and segment DF corresponds to arc DF.
As both segments are congruent, therefore, both arcs will be congruent as well.
We can represent this information as:
[tex]\text{ Arc RS}\cong \text{Arc DF}[/tex]
Therefore, option A is the correct choice.
What is the m∠ABC?
1)m∠ABC = 60°
2)m∠ABC = 67°
3)m∠ABC = 120°
4)m∠ABC = 127°
Answers
we are given
m∠BCD =67
and m∠BDC=60
we know that
m∠ABC is exterior angle
m∠BCD and m∠BDC are interior angles
exterior angle is sum of interior angles
so, we can write it as
m∠ABC=m∠BCD+m∠BDC
now, we can plug values
and we get
m∠ABC=60+67
m∠ABC=127
so, option-4.........Answer
Prism A is similar to Prism B. The volume of Prism A is 2080 cm³.
What is the volume of Prism B?
A.260 cm³
B.520 cm³
C.1040 cm³
D.16,640 cm³
Will give brainliest answer!
Answers
for two similar prisms, if the ratio of sides is a, the ratio of volume is a³
2080/260=8=2³
16640/2080=8=2³
2080/520=4, not a cubic number
2080/1040, not a cubic number
It is either A or D depending on which prism is bigger.
Final answer:
Prism B's volume is 8 times larger than Prism A's volume due to the dimensions being twice as large. Given the volume of Prism A as 2080 cm³, the volume of Prism B is 16640 cm³.
Explanation:
The student is asking about the volume of similar prisms. When two prisms are similar, their volumes are proportional to the cube of the ratio of their corresponding linear dimensions. In this case, Prism B is similar to Prism A, and the ratio of the volumes is given in the problem. Specifically, the volume of Prism B is 4 times the volume of Prism A because the dimensions of Prism B are twice that of Prism A, making the volume 23 or 8 times greater. However, you've also provided that the volume of Prism B is 4 times that of Prism A, this seems to be a conflict in the information, and there's an issue with typos in the provided content which makes it inconsistent (2L3 versus 213, 213). Based on the correct proportion which should be 8 times, if the volume of Prism A is 2080 cm3, then the volume of Prism B would be 2080 cm3 multiplied by 8 (8L3/L3), yielding 16640 cm3.
F(x) = x4/5(x − 6)2 find the critical numbers of the function
Answers
F(x) = x(4/5)(x-6)(2) = x(8/5)(x-6) = (8/5)(x^2 - 6x)
Taking the derivative:
F'(x) = (8/5)(2x - 6)
F'(x) = 0 at x = 3,
critical number = 3
Final answer:
To find the critical numbers, differentiate the function using the product rule, set the derivative equal to zero, and solve for x. Critical numbers are where the derivative is zero or undefined, provided they are within the domain of the function.
Explanation:
To find the critical numbers of the function f(x) = x4/5(x − 6)2, you need to locate the values of x where the first derivative of the function is either zero or undefined. The first derivative can be calculated using the product rule and the power rule.
First, let's find the derivative:
f'(x) = d/dx [x4/5] * (x - 6)2 + x4/5 * d/dx [(x - 6)2]
After simplifying, you will get a derivative function where you can then set it equal to zero to find the critical points. The points where the derivative is zero are potential local maxima, minima, or points of inflection. Additionally, points where the derivative is undefined can also be critical points, if they are within the domain of the function.
Once you calculate and simplify the derivative, set it equal to zero and solve for x. You might find that you get explicit values of x, which are the critical numbers of the function. If the function's derivative does not exist at some point, that will also be a critical number.
Remember, critical numbers are only relevant if they are within the domain of the original function.
helppppppppppppppppppppppp
Answers
We rewrite the polynomial:
2x ^ 2-4x + 7 = 0
Applying the resolver we have:
x = (- b +/- root (b ^ 2-4ac)) / 2a
x = (- (- 4) +/- root ((- 4) ^ 2-4 (2) (7))) / 2 (2)
x = (- (- 4) +/- root (16-56)) / 2 (2)
x = (- (- 4) +/- root (-40)) / 4
x = (2 +/- root (-10)) / 2
x = (2 +/- root (10) * i) / 2
Answer:
x = (2 +/- root (10) * i) / 2
option 3
The formula for volume of this rectangular prism is:
V = 2x 3 + 17x 2 + 46x + 40
Find an expression for the missing side length. Show all of your work for full credit.
Answers
[tex]V = (w) * (h) * (l) [/tex]
Where,
l: length
h: height
w: width
Substituting values we have:
[tex]2x ^ 3 + 17x ^ 2 + 46x + 40 = (w) * (x + 2) * (x + 4) [/tex]
From here, we clear the value of w.
[tex]w = (2x ^ 3 + 17x ^ 2 + 46x + 40) / ((x + 2) * (x + 4)) [/tex]
Factoring the numerator we have:
[tex]w = ((x + 2) * (x + 4) * (2x + 5)) / ((x + 2) * (x + 4)) [/tex]
Canceling similar terms we have:
[tex]w = 2x + 5 [/tex]
Answer:
The missing side is of length:
w = 2x + 5
The volume of a rectangular prism is the product of its dimension.
The missing side length is 2x + 5.
The volume is given as:
[tex]\mathbf{V = 2x^3 + 17x^2 + 46x + 40}[/tex]
Let the missing side be y.
So, we have:
[tex]\mathbf{V = (x + 2) \times ( x + 4) \times y}[/tex]
So, we have:
[tex]\mathbf{(x + 2) \times ( x + 4) \times y = 2x^3 + 17x^2 + 46x + 40}[/tex]
Factorize
[tex]\mathbf{(x + 2) \times ( x + 4) \times y = (x + 2) \times (x + 4) \times (2x +5)}[/tex]
Cancel out common factors
[tex]\mathbf{y = (2x +5)}[/tex]
Remove brackets
[tex]\mathbf{y = 2x +5}[/tex]
Hence, the missing side length is 2x + 5.
Read more about volumes at:
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The values √8 and √14 are plotted on the number line.
What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4
Answers
Answer:
The correct option is 2.
Step-by-step explanation:
The values √8 and √14 are plotted on the number line.
From the given number line it is clear that
[tex]\sqrt{8}\approx 2.8[/tex]
[tex]\sqrt{14}\approx 3.7[/tex]
We have to find the approximate difference in tenths between the two values √8 and √14.
[tex]\sqrt{14}-\sqrt{8}\approx 3.7-2.8[/tex]
[tex]\sqrt{14}-\sqrt{8}\approx 0.9[/tex]
The approximate difference in tenths between the two values is 0.9.
Therefore the correct option is 2.
Which of the following would be a factor of the equation above.
Answers
The factorization would be (7x +3)(x -3).
Which is the formula for the volume of a sphere with diameter d?
A. S= 4πd²
B. S= πd²
C. S= [tex] \frac{4}{3} [/tex]πd³
D. S= [tex] \frac{1}{6} [/tex]πd³
Answers
LM¯¯¯¯¯¯¯ is the midsegment of trapezoid ABCD . AB=78 and DC=142 . What is LM ?
Answers
LM = (AB +DC)/2
.. = (78 +142)/2
LM = 110
$7.80/hour = ____ cents/minute?
Answers
Your Welocme
Use the rules of significant figures to answer the following question:
67.31 - 8.6 + 212.198
A. 270.9
B. 271
C. 270.908
D. 270
Answers
Answer:
A. 270.9
Step-by-step explanation:
We know that the rule of significant figures for addition and subtraction states that 'the number of places after the decimal point in the result is equal to the least number of decimal places in each term.'
So, 67.31 - 8.6 + 212.198 = 67.31 + 212.198 - 8.6 = 279.508 - 8.6 = 270.908
Now, the resultant number is 270.908
Using the rule of significant figures, we get that, the number of places after the decimal point in 270.908 will be equal to the least number of decimal places i.e. 1 ( in 8.6 )
Hence, 67.31 - 8.6 + 212.198 = 270.9
Find an equation of the line that satisfies the given conditions. through (−1, −3); perpendicular to the line 2x + 7y + 2 = 0
Answers
2(-1) + 7(-3) + 2 = 0
-2 - 21 + 2 = 0
-21 = 0
PLEASE HELP
7.06
1. Find the first six terms of the sequence.
a1 = -7, an = 4 • an-1
A) -7, -28, -112, -448, -1792, -7168
B) -28, -112, -448, -1792, -7168, -28,672
C) -7, -28, -24, -20, -16, -12
D) 0, 4, -28, -24, -20, -16
2. Find an equation for the nth term of the arithmetic sequence.
-13, -8, -3, 2, ...
an = -13 x 5(n - 1)
an = -13 + 5(n - 1)
an = -13 + 5(n + 2)
an = -13 + 5(n + 1)
3. Find an equation for the nth term of the arithmetic sequence.
a15 = -53, a16 = -5
A) an = -725 - 48(n - 1)
B) an = -725 + 48(n + 1)
C) an = -725 + 48(n - 1)
D) an = -725 - 48(n + 1)
4. Determine whether the sequence converges or diverges. If it converges, give the limit.
11, 44, 176, 704, ...
A) Diverges
B) Converges; 231
C) Converges; 3751
D) Converges; 935
5. Find an equation for the nth term of the sequence.
-4, -16, -64, -256, ...
A) an = 4 • -4n
B) an = 4 • -4n + 1
C) an = -4 • 4n
D) an = -4 • 4n - 1
6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -2 and 16, respectively.
A) an = 1 • (-2)n - 1
B) an = 1 • 2n
C) an = 1 • (-2)n + 1
D) an = 1 • 2n - 1
7. Write the sum using summation notation, assuming the suggested pattern continues.
4 - 24 + 144 - 864 + ...
A) summation of four times six to the power of n from n equals zero to infinity
B) summation of four times negative six to the power of n from n equals zero to infinity
C) summation of four times negative six to the power of the quantity n minus one from n equals zero to infinity
D) summation of four times six to the power of the quantity n plus one from n equals zero to infinity
8. Write the sum using summation notation, assuming the suggested pattern continues.
-3 + 6 + 15 + 24 + ... + 132
A) summation of negative 27 times n from n equals 0 to infinity
B) summation of negative 27 times n from n equals 0 to 15
C) summation of the quantity negative 3 plus 9 n from n equals 0 to infinity
D) summation of the quantity negative 3 plus 9 n from n equals 0 to 15
9. Write the sum using summation notation, assuming the suggested pattern continues.
343 + 512 + 729 + 1000 + ... + n3
A) summation of the quantity n minus 1 cubed from n equals 7 to infinity
B) summation of n cubed from n equals 7 to infinity
C) summation of n cubed from n equals 8 to infinity
D) summation of the quantity n plus 1 cubed from n equals 7 to infinity
10. Find the sum of the arithmetic sequence.
3, 5, 7, 9, ..., 21
A) 39
B) 120
C) 20
D) 23
11. Find the sum of the geometric sequence.
4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3
A) 1363 divided by 3
B) 1364 divided by 15
C) 1364 divided by 3
D) 1363 divided by 15
12. An auditorium has 20 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 390
B) 580
C) 620
D) 400
13. Use mathematical induction to prove the statement is true for all positive integers n.
10 + 20 + 30 + ... + 10n = 5n(n + 1)
14. A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.
Answers
2. B. The sequence is -13, -8, -3, 2... It's obvious that each term is equal to the previous term plus 5. This is an arithmetic sequence with initial term -13 and common difference 5. We know a1=-13, so a_n=-13+5*(n-1). The answer is B.
3. A. We are given a15=-53, a16=-5. The common difference of the arithmetic sequence is -5-(-53)=48. The formula for a_n term is a1+48*(n-1). We know that a15=-13; plug in n=15, a15=-53=a1+48*(15-1), a1=-725. So a_n=-725+48*(n-1).
4. Diverge. We are given a few terms, 11, 44, 176, 704... Observe that each term is four times the previous one. 11*4=44, 44*4=176, 176*4=704... This is a geometric series with common ratio>1. You can keep multiplying by 4 and the series goes to infinity, so it diverges.
5. D. We have -4, -16, -64, -256... Same as above, each term is four times the previous one. The initial term is a1=-4. The common ratio d=4. So a_n=a1*d^(n-1)=-4*4^(n-1)=-4^n. (D).
6. The answer is A. a2=-2, a5=16. Suppose the common ratio is D. a_n=a1*d^(n-1). a2=a1*d; a5=a1*d^4. Plug in a2 and a5: -2=a1*d, 16=a1*d^4. 16/-2=d^3=-8, d=-2, a1=1. So a_n=1*(-2)^(n-1).
7. B. We are given the sequence 4, -24, 144,... Each term is -6 times the previous one. The first term a0=4, the n^th term a_(n-1) is a1*d^n=4*(-6)^n. To express the sum, we simply have to use the sigma notation and sum 4*(-6)^n from n=0 to infinity. The answer is B.
8. D. We are given -3 + 6 + 15 + 24... 132. Each term is equal to the previous one plus 9. First term a0=-3, n^th term a_n-1 is -3+9*n. The last term is 132. 132 =-3+9n, n=15. So we have to sum -3+9n from n=0 to n=15.
9. B. 343 + 512 + 729 + 1000+... 343=7^3, 512=8^3, 729=9^3, 1000=10^3. This is a sequence of perfect cubes. Therefore, the sum is n^3 from n=7 to infinity. (The initial term is 343=7^3).
10. B. We are given 3, 5, 7, 9, ... 21. The common difference is 2. There are (21-3)/2+1=10 terms. The initial term a1=3, and last term is a10=21. The sum is (a1+a10)*10/2=(3+21)*10/2=120.
11. C. 4/3, 16/3, 64/3, 256/3, 1024/3. Each term is four times the previous one. This is a geometric series with initial term a1=4/3 and common ratio r=4. 1024/3 is the 5th term of the sequence. So sum=a1*(1-r^n)/(1-r)=4/3*(1-4^5)/(1-4)=-4/9*-1023=1364/3.
12. B. 10,12,14,... This is an arithmetic sequence. a1=10, and common difference d=2. There are 20 terms (20 rows). a20=a1+d*(n-1)=10+2*(20-1)=48. So the sum S=(a1+an)*n/2=(10+48)*20/2=580.
13. 10 + 20 + 30 + ... + 10n = 5n(n + 1). When n=1, this expression is true, since 10=5*1*(1+1). Suppose when n=k, this statement is true, then when n=k+1, the left side is 10+...+10n+10(n+1), the right side is 5(n+1)(n+2). The left side adds 10(n+1) compared to the previous one. The right side adds 5(n+1)(n+2)-5n(n+1)=5(n+1)(n+2-n)=10(n+1). So the statement holds true.
14. The height at week 0 is a0=300 (initial height). Common difference is 4.2 (weekly increment). a_n=300+4.2n. At week n, the height of the tree is 300+4.2*n centimeters.
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Boyles law involves the pressure and volume of gas in a container. It can be repersented by the formula p sub 1 v sub 1= p sub 2 v sub 2. When the formula is solved for p sub 2, the results is
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Boyle's Law can be rearranged to solve for p sub 2 (final pressure) using the formula p sub 2 = p sub 1 v sub 1 / v sub 2. This shows the inverse relationship between pressure and volume of gas at a constant temperature.
Explanation:The question is asking to solve the formula representing Boyle's Law (p sub 1 v sub 1 = p sub 2 v sub 2) for p sub 2. Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature is held constant. To solve for p sub 2, you rearrange the formula to be p sub 2 = p sub 1 v sub 1 / v sub 2. This formula means that the final pressure (p sub 2) equals the initial pressure (p sub 1) times the initial volume (v sub 1), all divided by the final volume (v sub 2). Therefore, if the volume increases, the pressure decreases, and if the volume decreases, the pressure increases, keeping the gas's temperature constant.
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a business analyst makes 20$ an hour for the first 42 hours he works during a week and 28$ an hour for each worked over 42 hours. which piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week
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Answer:
[tex]y=28(x-42)+840[/tex]
Step-by-step explanation:
Let he works for x hours in total.
We are given that he makes 20$ an hour for the first 42 hours
So, he earns in 1 hour = 20
He earns in 42 hours = [tex]20 \times42[/tex]
= [tex]840[/tex]
Now we are given that he earns $28 an hour for each hour worked over 42 hours.
Since he worked for 42 hours out of x hours .
So, remaining hours = x-42 hours
So,he earns for x-42 hours = [tex]28\times(x-42)[/tex]
y denotes his total earning of weekly
So, total earning [tex]y=28(x-42)+840[/tex]
Hence piecewise equation models his weekly pay y in dollars as it relates to the number of hours x that he has worked during the week is [tex]y=28(x-42)+840[/tex]
An architect created plans for a house using a scale factor of 1:16 . In the plans, the floor of the house has an area of 7 square feet. What is area of the floor in the actual house? Enter your answer in the box.
A rectangle has a length of 6 inches and a width of 3 inches.
What is the effect on the perimeter when the dimensions are multiplied by 8?
The perimeter is increased by a factor of 8.
The perimeter is increased by a factor of 24.
The perimeter is increased by a factor of 64.
The perimeter is increased by a factor of 256.
This figure is made up of a triangle and a semicircle.
What is the area of this figure?
Use 3.14 for pi. Round only your final answer to the nearest tenth.
Enter your answer, as a decimal, in the box.
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the area is 7 square feet
when calculating the area the scale factor is squared as well.
since the scale factor is 16, to find out area the scale should be squared that is,
16*16 = 256
then the new area is 7 square feet * 256
actual area = 256 * 7 = 1792 square feet
Q2. the rectangle with length 6 inches and width 3 inches.
the perimeter of the rectangle before changing dimensions are;
=(6*2) + (3*2)
= 12 + 6 = 18 inches
after multiplying the dimensions by 8,
new length = 6*8 = 48 inches
new width = 3*8 = 24 inches
new perimeter = (48*2) + (24*2)
= 96 + 48
= 144 inches
the perimeter ratio from new to old = 144:18
the perimeter has increased by (144/18) times
= 144/18 = 8
answer is perimeter increased by a factor of 8
q3)
area of the triangle
= 1/2 * height * base
= 1/2 * (5-2) *(4-(-3))
= 1/2 * 3 * 7
= 10.5 units²
area of semicircle
=pi*r2
r = 2-(-1.5)
= 3.5
area = 3.14 * (3.5)²
= 38.465 units²
total area = area of triangle + area of semicircle
= 10.5 + 38.465
= 48.965
round it off to the closest tenth
area = 49 units²
Between the ages of 24 months and 6 years, the average child will gain _____ in height. 1 foot 1.5 feet 8 inches 4 inches
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3in*4years =12in or 1 foot
Could use some help!
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0<= x < ∞
A sandwich shop uses the box size shown to pack boxed lunches. They have determined that they need to use bigger boxes. If the side lengths of the square faces are changed to 7 inches, by how much will this increase the volume of the box?
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We do the same for the new shape, which now has a 7 in place of the 5. So 7x7x10=490.
Lastly, we subtract the volume of the new shape from the volume of the old shape to see the difference. So, 490-250=240.
So the answer to this is 240.
Answer:
240 cubic cm
Step-by-step explanation:
Volume of the box before increament in sides = length*width*height
Length= 5 in.
Width=5 in.
Height = 10 in.
Putting these vales in formula
Volume of box = 5*5*10
=[tex]250cm^{3}[/tex]
Now If the side lengths of the square faces are changed to 7 inches,
So, Length will be 7 in.
Width will be 7 in.
So, new volume = 7*7*10
=[tex]490cm^{3}[/tex]
Thus increase in volume = 490-250 =240
Hence by 240 cubic cm will this increase the volume of the box
need help thank thank you
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Find the area of A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
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where:
[tex]V[/tex] is the volume
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
From the question we know that [tex]A=175[/tex] and [tex]h=7[/tex]. Lets replace those values in our volume formula:
[tex]175= \pi r^{2} 7[/tex]
Now we can solve for [tex]r[/tex] to find our radius:
[tex]r^{2} = \frac{175}{7 \pi } [/tex]
[tex]r^{2} = \frac{25}{ \pi } [/tex]
[tex]r= \sqrt{ \frac{25}{ \pi } } [/tex]
[tex]r= \frac{5}{ \sqrt{ \pi } } [/tex]
Now that we know the radius, we can use the formula for the area of a cylinder [tex]A=2 \pi rh+2 \pi r^{2} [/tex]
where:
[tex]A[/tex] is the area
[tex]r[/tex] is the radius
[tex]h[/tex] is the height
We know now that [tex]r= \frac{5}{ \sqrt{ \pi } } [/tex] and [tex]h=7[/tex], so lets replace those values in our area formula:
[tex]A=2 \pi ( \frac{5}{ \sqrt{ \pi } } )(7)+2 \pi ( \frac{5}{ \sqrt{ \pi } })^{2} [/tex]
[tex]A= \frac{70 \pi }{ \sqrt{ \pi } } +50[/tex]
[tex]A=174.07[/tex]
We can conclude that the area of a cylinder that has a volume of 175 cubic units and a height of 7 units is 174.07 square units.